Estimation of the best constant involving the $L^2$ norm of the higher-order Wente problem

Abstract

We study the best constant involving the $L^2$ norm of the $p$-derivative solution of Wente's problem in ${ℝ}^{2p}$. We prove that this best constant is achieved by the choice of some function $u$. We give also explicitly the expression of this constant in the special case $p=2$.